## ELEMENTARY SYNTHETIC GEOMETRY OF THE POINT, LINE AND CIRCLE IN THE PLANE |

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Page 4

In this example there is but one X (the greater side) and one Y (the greater

, and as X is (corresponds to or is opposite) Y ... Every point equidistant from the

end-points of a linesegment is on the

In this example there is but one X (the greater side) and one Y (the greater

**angle**), and as X is (corresponds to or is opposite) Y ... Every point equidistant from the

end-points of a linesegment is on the

**right**bisector of that segment, - SECTION I. Page 17

One-half of a circumangle is a s/raigh/ angle, and onefourth of a circumangle is a

the adjacent angles formed is a circumangle. OA, OB, OC, ..., OF are lines ...

One-half of a circumangle is a s/raigh/ angle, and onefourth of a circumangle is a

**right angle**. 37°. 7/leorem.–If any number of lines meet in a point, the sum of allthe adjacent angles formed is a circumangle. OA, OB, OC, ..., OF are lines ...

Page 18

If a radius vector be rotated until its direction is reversed it describes a straight

angle. And conversely, if a radius ... If A A = A_B, then A A' = 4 B = A_B', and all

four angles are equal, and each is a

If a radius vector be rotated until its direction is reversed it describes a straight

angle. And conversely, if a radius ... If A A = A_B, then A A' = 4 B = A_B', and all

four angles are equal, and each is a

**right angle**(36°). Therefore, if two adjacent ... Page 19

A

...

A

**right angle**is denoted by the symbol T. The symbol L also denotes two**right****angles**or a straight angle. Des. 3.--When two angles together make up a**right****angle**they are com//ementary to one another, and each is the complement of the...

Page 20

The angles BOC and COA are each

not a

OC is the only perpendicular. perpendicular can be drawn to the line. o (/.é. (.

The angles BOC and COA are each

**right angles**(40°, Def. 2). Therefore BOD isnot a

**right angle**, and OD is not LAB. But OD is any line other than OC. ThereforeOC is the only perpendicular. perpendicular can be drawn to the line. o (/.é. (.

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### Common terms and phrases

ABCD algebraic altitude base becomes called centre centre-line chord circle coincide collinear common concurrent congruent considered constant construct Converse corresponding cuts denote describe determine diagonals diameter difference direction distance divided draw drawn equal expressed external figure fixed point four geometric given given line given point gives greater harmonic Hence internal intersect inverse joins length lies line-segment mean measure median meet middle point opposite opposite sides orthogonally pair parallel passes pencil perpendicular perspective placed plane polar polygon position Proof proved quadrangle radical axis radius range ratio reciprocal rectangle regular relation remaining respect right angle right bisector rotation segment sides similar Similarly similitude square straight symbol taken tangent theorem touch triangle vertex vertices

### Popular passages

Page 176 - The square described on the hypothenuse of a rightangled triangle is equal to the sum of the squares described on the other two sides.

Page 183 - The sides of a triangle are proportional to the sines of the opposite angles.

Page 260 - Three lines are in harmonical proportion, when the first is to the third, as the difference between the first and second, is to the difference between the second and third ; and the second is called a harmonic mean between the first and third. The expression 'harmonical proportion...

Page 19 - Every circumference of a. circle, whether the circle be large or small, is supposed to be divided into 360 equal parts called degrees. Each degree is divided into 60 equal parts called minutes, and each minute into 60 equal parts called seconds.

Page 77 - J_ to the given line. .'. the construction gives the perpendicular to a given line at a given point in the line.

Page 122 - And conversely, if the square on one side of a triangle is equal to the Bum of the squares on the other two sides, the angle contained by these two sides is a right angle.

Page 124 - The difference of the squares of two sides of a triangle is equal to the difference of the squares of the segments made by the altitude upon the third side.